Dice & Cube

Dice and Cube is a topic where a cube or dice is shown in different positions and you have to find which number or letter is on the opposite face or hidden face. It is a visual and spatial topic that requires practice to master.

Basic Facts About a Dice:

• A standard dice has 6 faces
• Opposite faces of a standard dice always add up to 7
• 1 is opposite to 6
• 2 is opposite to 5
• 3 is opposite to 4

Important Rule: In SSC CGL questions, the dice shown may NOT be a standard dice. So do not always use the "sum = 7" rule. Always find the opposite faces from the given positions.

Types of Dice & Cube Questions in SSC CGL:

Type 1 - Finding Opposite Face Two or three positions of a dice are shown and you have to find which face is opposite to a given face.

Example: 

Position 1: Top = 1, Front = 2, Right = 3 

Position 2: Top = 2, Front = 4, Right = 5

Find the face opposite to 1.

Method: 

In Position 1: Top = 1, so Bottom = opposite of 1 

In Position 2: Top = 2 - this is the Front face of Position 1 

Compare the two positions to trace which face moved where.

Common faces in both positions help identify opposites.

Type 2 - Open Dice (Unfolded Cube) An unfolded cube (net) is shown and you have to find which face will be opposite to which face when folded.

Example:

      [2]
   [1][3][4][5]
      [6]

When folded:

• 3 is in the center row middle - it is opposite to the face directly across
• 1 is opposite to 5 (they are at opposite ends of the middle row)
• 2 is opposite to 6 (top and bottom of center column)
• 3 is opposite to 4... wait, 3 and 4 are adjacent so they cannot be opposite

Always trace the folding carefully.

Type 3 - Painted Cube A large cube is painted on all sides and then cut into smaller cubes. Questions ask how many small cubes have 0, 1, 2, or 3 painted faces.

Example: A cube of side 3 units is painted red on all faces and then cut into 27 small cubes (3×3×3).

How many small cubes have:

• 3 painted faces = Corner cubes = 8 (always 8 for any size)
• 2 painted faces = Edge cubes = 12 × (n-2) = 12 × 1 = 12
• 1 painted face = Face cubes = 6 × (n-2)² = 6 × 1 = 6
• 0 painted faces = Inner cubes = (n-2)³ = 1³ = 1

Total = 8 + 12 + 6 + 1 = 27

Formula for Painted Cube of side n cut into n³ small cubes:

• 3 painted faces (corners) = 8
• 2 painted faces (edges) = 12 × (n-2)
• 1 painted face (faces) = 6 × (n-2)²
• 0 painted faces (inner) = (n-2)³

Type 4 - Dice Stacking Multiple dice are stacked and you have to find the total of hidden faces.

Example: 

Three dice are stacked. Find the total of all hidden touching faces.

Logic: 

When two dice touch, the touching faces of both dice are hidden. 

Two touching faces of adjacent dice always add up to 7 (if standard dice). 

Three dice stacked = 2 pairs of touching faces = 2 × 7 = 14

How to Solve Dice Questions:

Step 1 - Look at two positions of the dice that share a common face. 

Step 2 - The common face helps you fix the orientation. 

Step 3 - Rotate the dice mentally from position 1 to position 2. 

Step 4 - The face that was on top in one position cannot be opposite to itself. 

Step 5 - Eliminate faces that are adjacent to find the opposite face.

Quick Tricks:

Trick 1 - If a face appears in both positions of the dice, it is NOT the answer (it cannot be opposite to itself).

Trick 2 - In an open dice, the face directly opposite in the cross shaped net is always the opposite face.

Trick 3 - For painted cube questions, always use the formula. Do not count manually.

Trick 4 - Corner cubes always have 3 painted faces and there are always exactly 8 corners in any cube.

Important Tips:

• Practice visualizing 3D objects mentally - this comes with practice
• For open dice questions, physically fold the net on paper to check
• Always verify painted cube answers using total = n³
• 1 to 2 questions come from this topic in SSC CGL every year
• Dice questions seem hard but become easy with 15-20 questions of practice